Morphometric distribution of depth and basin shape in Aotearoa New Zealand lakes

Using machine learning to improve national lake depth predictions

Tadhg Moore, Chris McBride, Deniz Özkundakci, Mathew Allen, Moritz K Lehmann, Matthew J Prentice, Whitney Woelmer, Maggie Armstrong, Kevin Rose

2024-11-19

Motivation

  • Developing the Lake Ecosystem Research New Zealand modelling platfom (LERNZmp).
  • Lake depth and morphometry are key drivers of lake ecosystem function, therefore accurate depth data is essential (Ganz, Glines, and Rose 2024).
  • The Freshwater Ecosystems New Zealand (FENZ) database is the most comprehensive database of lake morphometry in New Zealand, but is limited in its depth data.
  • NZ lakes provide a unique opportunity to develop a comprehensive database of lake depth and morphometry, particularly given the diversity of lake size, depth and geomorphic type.

Objectives

  • Develop a comprehensive database of lake depth and morphometry for New Zealand.
  • Use machine learning to predict mean and maximum lake depth from this data.
  • Compare these predictions to the FENZ database and other global lake depth databases e.g. maximum lake depths - GLOBathy(Khazaei et al. 2022) and mean lake depth - HydroLAKES (Messager et al. 2016)

FENZ Lakes

  • Lack of a central database on lake morphometry, particularly depth
  • Large number of bathymetric data has been recorded across lakes in New Zealand
  • Current predictions of max lake depth, within the FENZ database (n=3475) are limited and have clear biases
Figure 1: Depth distribution of FENZ lakes. The x-axis is log10 scaled.

Bathymetry example: Lake Rotoma

Depth contours

Figure 2: Depth contours of Lake Rotoma, a large lake in the Bay of Plenty region.

Bathymetry example: Lake Rotoma

Bathymetry raster

Figure 3: Depth raster of Lake Rotoma, a large lake in the Bay of Plenty region.

Bathymetry example: Lake Rotoma

Estimated hypsographic curve

Figure 4: Three dimensional rendering of Lake Rotoma’s bathymetry.

Bathymetry example: Lake Rotoma

Estimated hypsographic curve

Figure 5: Hypsograph curve of Lake Rotoma.

Hypsographic summary

Table 1: Hypsographic summary of Lake Rotoma
Variable Value
Max depth 90.25
Mean depth 45.43
Volume development index 1.51
Area (ha) 1063.27
Shoreline length (km) 23.40
Shoreline development index 2.04

Lakes with bathymetry data

  • Lakes with bathymetric data are relatively evenly distributed across New Zealand.
  • Lake geomorphic type is highly regionalised.
Figure 6: Map of lakes with bathymetric data and maximum depth data in New Zealand. Lakes with bathymetry data have a black marker.

Methods

  • Bathymetry survey data were sourced from a variety of sources - paper maps, digital files, and online databases (n=.
  • Shoreline data were updated using satellite and aerial imagery.
  • Depth data were interpolated using a Multilevel B-Spline Approximation (MBA) algorithm.
  • Hypsographic curves were calculated for each lake.
  • Comparison of depth and area with other databases.
  • Used machine learning to predict lake depth from morphometric data for all lakes in New Zealand and benchmark against the FENZ dataset.

Depth-area relationship

Figure 7: Summary of measured lake area and max depth by latitude and elevation.

Depth-area x geomorphic type

Figure 8: Summary of measured lake area and max depth by geomorphic type.

Distribution of volume development

Development of Volume, \(D_V\) (Hutchinson 1957) is a measure of departure of the shape of the lake basin from that of a cone calculated using the maximum depth \(Z_{max}\) and the average depth \(\bar{Z}\) :

\[D_V = \frac{3 \times \bar{Z}}{Z_{max}}\]

For the majority of lakes, DV >1 (i.e. a conical depression). DV is greatest in shallow lakes with flat bottoms.

Figure 9: Distribution of volume development (DV) by geomorphic type.

Predicting mean and max depth

Figure 10: Predicted vs observed max depth. Note that the x and y axes are log10 scaled.
Table 2: Model fit for max depth
Source N Bias RMSE R2
FENZ 183 -0.79 44.64 0.70
GloBATHY 119 20.93 72.68 0.43
ML model 190 -0.49 19.17 0.95
Figure 11: Predicted vs observed mean depth. Note that the x and y axes are log10 scaled.
Figure 12: Predicted vs observed mean depth. Note that the x and y axes are log10 scaled.
Table 3: Model fit for mean depth
Source N Bias RMSE R2
FENZ 155 6.24 21.59 0.71
Hydrolakes 91 7.27 22.48 0.79
ML model 155 -0.15 7.80 0.97

Machine learning

Bathymetric data from 156 lakes were digitised and collated for use in this study.

Using a machine learning model, we were able to predict maximum lake depth from morphometric data with an \(r^2\) = 0.95 and mean lake depth with an \(r^2\) = 0.97.

This was substantially better than the FENZ dataset, which had an \(r^2\) = 0.7 for max depth and 0.71 for mean depth.

Applications

  • Predicted depth data is used in the LERNZmp for lakes without bathymetric data.
  • Highlights lakes with limited depth data for future surveying.
  • Provides a comprehensive database of lake depth and morphometry for Aotearoa New Zealand for future research.

References

Ganz, Keenan J., Max R. Glines, and Kevin C. Rose. 2024. “The Distribution of Depth, Volume, and Basin Shape for Lakes in the Conterminous United States.” Limnology and Oceanography 69 (1): 22–36. https://doi.org/10.1002/lno.12475.
Khazaei, Bahram, Laura K. Read, Matthew Casali, Kevin M. Sampson, and David N. Yates. 2022. “GLOBathy, the Global Lakes Bathymetry Dataset.” Scientific Data 9 (1): 36. https://doi.org/10.1038/s41597-022-01132-9.
Messager, Mathis Loïc, Bernhard Lehner, Günther Grill, Irena Nedeva, and Oliver Schmitt. 2016. “Estimating the Volume and Age of Water Stored in Global Lakes Using a Geo-Statistical Approach.” Nature Communications 7 (1): 13603. https://doi.org/10.1038/ncomms13603.